After C&L notification
Once you have notified one or more substances to the Classification and Labelling (C&L) Inventory, your classification will be published on the C&L database via the ECHA website, which can be accessed directly here: https://echa.europa.eu/information-on-chemicals/cl-inventory-database .
Your company will not be publicly identified on the C&L Inventory, as this simply lists the number of companies who have made the same notification. There is also no public identification of the tonnage bands made or imported into the EU.
ECHA expect that the C&L notification will be kept up to date, so if you find out new information on the hazard classification for a substance, or the tonnage band alters, you are expected to go in an amend the notification.
The most likely scenario for a change in the hazard classification of a substance is when it goes through REACH registration. This process may reveal new hazards, or an alteration in the level of existing hazards, different to your original notification, and in this case, you should consider altering your notification to agree with the REACH registration (if applicable, e.g. you have the same level of impurities etc).